You have been hired to design a gasoline tank. The tank is in the shape of a right cylinder and needs to hold 100,000 liters. The tank will be constructed using two sheets of metal. One sheet will be rolled into a cylinder. The other sheet will have two circles cut from it. Prior to welding the inside will be coated with two layers of rust protection and the outside will be coated with three layers of rust protection and a coat of paint. The paint costs $0.23 per square meter and the rust protection costs $0.45 per square meter. It costs $0.20 per meter to roll the cylinder, $0.30 per meter to weld the pieces together, and $0.35 per meter to cut the circles. The material for the side costs $2.50 per square meter and the material for the top and bottom costs $5.00 per square meter.
Find a formula for the cost of the tank in terms of radius and then find the radius that optimizes the cost. Include the dimensions of the tank.

a) What is the formula for the total cost of the tank in terms of radius? (the easiest way to approach this is to break the problem up into the component costs like cost of material, cost of rolling, cost of cutting, etc. and then add them up.)

b) What is the radius and height that minimizes cost?

c) What is the cost of producing one tank?